The hypotenuse of a right triangle is 17 cm long. Another side of the triangle is 7 cm longer than the third side. How do you find the unknown side lengths?

2 Answers
Jun 2, 2018

8 cm and 15 cm

Explanation:

Using the Pythagorean theorem we know that any right triangle with sides a, b and c the hypotenuse:

a^2 + b^2 = c^2

c=17

a = x

b = x+7

a^2 + b^2 = c^2

x^2 + (x+7)^2 = 17^2

x^2 + x^2 +14x + 49 = 289

2x^2 +14x = 240

x^2 +7x -120 = 0

(x + 15) (x - 8)=0

x=-15

x=8

obviously the length of a side cannot be negative so the unknown sides are:

8

and

8+7=15

Jun 2, 2018

8" and "15

Explanation:

"let the third side "=x

"then the other side "=x+7larrcolor(blue)"7 cm longer"

"using "color(blue)"Pythagoras' theorem"

"square on the hypotenuse "=" sum of squares of other sides"

(x+7)^2+x^2=17^2

x^2+14x+49+x^2=289

2x^2+14x-240=0larrcolor(blue)"in standard form"

"divide through by 2"

x^2+7x-120=0

"the factors of - 120 which sum to + 7 are + 15 and - 8"

(x+15)(x-8)=0

"equate each factor to zero and solve for x"

x+15=0rArrx=-15

x-8=0rArrx=8

x>0rArrx=8

"lengths of unknown sides are"

x=8" and "x+7=8+7=15